Coherent tunnelling adiabatic passage in optical fibres using superimposed long-period fiber gratings

Abstract

In this paper, we present the optical analogue of stimulated Raman adiabatic passage (STIRAP) technique for three level atomic system in optical fibre geometry. Considering linearly polarized modes of an optical fibre, it is shown that using a pair of superimposed long-period gratings with peak refractive index perturbation varying spatially along the propagation axis, light can be transferred adiabatically from one core mode to another core mode via an intermediate cladding mode which itself does not get appreciably excited; thus acting like a dark mode. We compare the transmission spectrum of superimposed long-period gratings involved in adiabatic transfer with the transmission spectrum of conventional long-period grating. The analogue output is further analysed for its tolerance to the changes in the ambient refractive index, temperature and other fabrication parameters.     

Dispersion control with use of long-period fiber gratings

Chirped long-period fiber gratings are analyzed for management of dispersion in optical fiber communications systems. A ray model is used to derive simple analytic expressions that describe the transmission, chromatic delay, and dispersion properties of chirped long-period fiber gratings. A numerical model based on coupled-mode theory is used to verify the accuracy of the analytic expressions and explore design issues of the chirped long-period grating. With certain reasonable restrictions, chirped long-period gratings are found to be a viable and desirable alternative to existing dispersion compensation techniques.     

A Novel Fiber-Optic Tapered Long-Period Grating Sensor for Pressure Monitoring

The method and the required installations for fabricating tapered long-period fiber gratings can be simpler than that of standard fiber Bragg gratings, and the fabrication process is faster. To our knowledge, the tapered long-period fiber grating pressure sensor is presented here for the first time. In this paper, the fabrication method for tapered long-period fiber gratings, the sensing principle, the sensor structure, the measurement setup, and the preliminary results are presented and discussed. The pressure sensitivity of the sensor is as high as 5.1 pm/bar.     

Transfer-matrix approach based on modal analysis for modeling corrugated long-period fiber gratings

A transfer-matrix method is developed for modeling a corrugated long-period fiber grating. Cladding-mode resonance in such a corrugated structure can be controlled by the applied tensile stress based on the photoelastic effect. A first-order vectorial perturbation expansion is used to derive the mode fields of the two basic regions under the strain-induced index perturbation. Because the etched cladding radius is much smaller than the unetched radius, the effect of the corrugated structure on cladding modes cannot be treated as a small perturbation. Thus the conventional coupled-mode theory is inadequate for the modeling of such a structure. Based on a self-consistent mode-matching technique, mode coupling within the corrugated structure can be described by a set of transfer matrices. We apply the formulation to the calculation of the transmission spectra of a corrugated long-period grating and compare the calculated with the experimental results. The transfer-matrix approach is found to account well for the features of the transmission spectra of the corrugated long-period gratings.     

Ultra-widely tunable long-period holey-fiber grating by the use of mechanical pressure

We report an ultra-widely tunable long-period holey-fiber grating, which combines the wide-range single-mode behavior and transverse strain sensitivity of the holey fibers with the advantages of mechanically induced long-period fiber gratings. We obtain a versatile widely tunable long-period holey-fiber grating with attractive transmission spectral characteristics for optical communications, fiber-based amplifiers, and lasers. The mechanically induced long-period holey-fiber grating shows a continuous tuning range over 500 nm, more than 12 dB depth notches with less than 0.75 dB out-of-band losses, and bandwidth control from 10 to 40 nm.     

Reconstruction of a fiber Bragg grating from noisy reflection data

We develop a novel method that enables one to reconstruct the structure of highly reflecting fiber Bragg gratings from noisy reflection spectra. When the reflection spectrum is noisy and the grating reflectivity is high, noise in the Bragg zone of the reflection spectrum is amplified by the inverse scattering algorithms and prevents the reconstruction of the grating. Our method is based on regularizing the reflection spectrum in frequencies inside the Bragg zone by using the data on the grating spectrum outside the Bragg zone. The regularized reflection spectrum is used to reconstruct the grating structure by means of inverse scattering. Our method enables one to analyze gratings with a high reflectivity from a spectrum that contains a high level of noise. Such gratings could not be analyzed by using methods described in previous work [IEEE J. Quantum Electron. 39, 1238 (2003)].     

Control of the characteristics of a long-period grating by cladding etching

We have analyzed the effects of the fiber cladding radius on the characteristics of long-period fiber gratings. By etching the cladding of a common single-mode fiber, we verified the characteristics experimentally. When by etching we reduce the cladding radius of a common single-mode fiber on which a long-period refractive-index modulation has been imposed, the coupling strength of the core and the cladding modes increases. In addition, the difference in the propagation constants (for a fixed wavelength) between the core mode and the cladding modes increases; hence the resonant transmission dip wavelengths shift to longer wavelengths. The proposed method can be useful in making and detuning long-period fiber grating filters.     

Synthesis of birefringent reflective gratings

The layer-peeling method for reconstruction of fiber and waveguide gratings is extended to the case of birefringent reflective gratings with polarization-dependent background index and polarization-dependent effective index contrast. Using a discrete grating model, we characterize the set of possible reflection and transmission Jones matrices and show that for a given wavelength, the total structure can be represented by a discrete reflector sandwiched between two retardation sections. In reflection the discrete reflector acts as a partial polarizer. A method for designing birefringent gratings is developed and tested numerically.     

Transfer-matrix method based on a discrete coupling model for analyzing uniform and nonuniform codirectional fiber grating couplers

A simple and efficient transfer-matrix method based on a discrete coupling model is presented to analyze uniform and nonuniform fiber grating couplers between copropagating core and cladding modes. Uniform and piecewise-uniform long-period gratings were fabricated by a point-by-point arc discharge technique. Their measured transmission spectra were compared with the transmission spectra calculated by the presented method.     

相移长周期光栅在EDFA增益平坦中的应用

对相移长周期光栅进行了理论分析,在此基础上,运用传输矩阵法对它的透射光谱进行数值计算,分析了相移量大小、平均折射率变化以及光栅长度等结构参数变化对相移长周期光栅透射谱的影响,并根据这些变化规律适当调节它的结构参数,使其透射光谱与平坦EDFA的目标光谱在一定程度上相符。平坦后的EDFA增益谱在34nm范围内最大波动不超过±0.7dB。根据此方法设计的增益平坦滤波器只包含一个器件,体积小,便于制造和封装,具有很好的市场应用前景。     

Embedded corrugated long-period fiber gratings for sensing applications

We demonstrate a method to make possible the mass production of corrugated long-period fiber gratings (C-LPFGs) by utilizing imprint lithography on polycarbonate (PC) substrates. For such C-LPFGs whose working principle is based on photoelastic effect, pretensile tension is required to be applied to inducing periodical refractive index variation. We then present an attempt to use PC as embedding material for providing internal compressive stress for C-LPFGs to have a photoelastic effect. This type of LPFG, termed embedded corrugated long-period fiber gratings (EC-LPFGs), is obtained after reimprinting the C-LPFGs into other PC substrates. Since compressive stress is retained due to the materials of different coefficients of thermal expansion (CTE), unlike C-LPFGs, EC-LPFGs can serve as strain, bending, and temperature sensors without the need of pretensile strain. The two most troublesome problems, the fragility of an etched fiber grating and the requirement of pretensile strain, can be simultaneously alleviated or solved by EC-LPFGs.     

Dependence of fringe spacing on the grating separation in a long-period fiber grating pair

The spectral spacing of the interference fringes formed by a pair of long-period fiber gratings was investigated. The variation of the fringe spacing was measured while the separation between the gratings was changed from 22 to 500 mm. When the grating separation was much longer than the length of the individual grating, the inverse of the fringe spacing became linearly proportional to the grating separation and to the differential effective group index of the fiber. In the third stop band of the grating pair, made along a dispersion-shifted fiber centered at 1.55 mum, the differential effective group index was calculated to be ~6.4 x 10(-3), which is approximately twice the differential effective index of the fiber. The discrepancy between the two indices was observed to decrease with the band order, a phenomenon that is explained by the first-order dispersion of the fiber. The measured interference fringes were not regularly spaced in the frequency domain, but regular spacing is required in wavelength-division multiplexing communication systems. Analysis of the second-order dispersion of the fiber and the grating-induced nonlinear phase shift within grating regions as the factors that induce chirping on the fringe spacing is presented.     

Self-imaging of gratings with rough strips

We analyze the self-imaging process produced by a transmission grating whose strips present two different roughness levels. This kind of grating periodically modulates the transmitted light owing only to the different microtopographic properties of the strips. In spite of the fact that the grating is not purely periodic, it produces a kind of self-image at Talbot distances. These self-images gradually appear as light propagates, but they are not present just after the grating, as occurs in amplitude or phase gratings. There exists a distance from the grating, which depends on the stochastic properties of roughness, from which the contrast of the self-images becomes stable. Important cases are analyzed in detail, such as low- and high-roughness limits. We assume for the calculations that the grating can be used in a mobile system. Simulations using the Rayleigh-Sommerfeld regime have been performed, which confirm the validity of the theoretical approach proposed in this work.     

Extreme-ultraviolet efficiency measurements of freestanding transmission gratings

We report new, near-normal-incidence, transmission grating efficiency results at selected extreme-ultraviolet wavelengths between 4.5 and 30.5 nm for two transmission gratings, one with a period of 200 nm and the other with a period of 400 nm. These gratings consist of opaque gold bars separated by open spaces that have been produced by photolithography techniques commonly used to produce electronic components. The gold bars and the open spaces are nominally of the same width. Both gratings have a thickness of 470 nm. The transmission efficiency at the central, first, and, when possible, second order of diffraction was measured. In addition, guided-wave phenomena at nonnormal angles of incidence, as well as transmission differences depending on which side of the grating was illuminated, were investigated. The observed guided-wave effects allow one to selectively enhance the transmission of the grating at desired wavelengths, as is realized with a blazed reflection grating.     

Extreme-ultraviolet radiation filtering by freestanding transmission gratings

Measurement of energetic neutral atoms fluxes in space requires efficient suppression of exceptionally strong background extreme-ultraviolet (EUV) and UV radiation. Diffraction filters make it possible to separate (transmit) charged and neutral particles from the background radiation (which would be suppressed). Recently developed freestanding transmission gratings look especially promising for implementation in a new family of diffraction EUV/UV filters. The first results of our experimental study of filtering properties of freestanding transmission gratings with a period of 200 nm are presented. The grating transmission was measured in the 52-131-nm wavelength range, and grating polarization properties were determined at 58.4 nm. It is shown that transmission gratings can be used efficiently as filters and polarizers in the EUV/UV spectral range.     

Diffraction efficiency of 200-nm-period critical-angle transmission gratings in the soft x-ray and extreme ultraviolet wavelength bands

We report on measurements of the diffraction efficiency of 200-nm-period freestanding blazed transmission gratings for wavelengths in the 0.96 to 19.4 nm range. These critical-angle transmission (CAT) gratings achieve highly efficient blazing over a broad band via total external reflection off the sidewalls of smooth, tens of nanometer thin ultrahigh aspect-ratio silicon grating bars and thus combine the advantages of blazed x-ray reflection gratings with those of more conventional x-ray transmission gratings. Prototype gratings with maximum depths of 3.2 and 6 μm were investigated at two different blaze angles. In these initial CAT gratings the grating bars are monolithically connected to a cross support mesh that only leaves less than half of the grating area unobstructed. Because of our initial fabrication approach, the support mesh bars feature a strongly trapezoidal cross section that leads to varying CAT grating depths and partial absorption of diffracted orders. While theory predicts broadband absolute diffraction efficiencies as high as 60% for ideal CAT gratings without a support mesh, experimental results show efficiencies in the range of ～50-100% of theoretical predictions when taking the effects of the support mesh into account. Future minimization of the support mesh therefore promises broadband CAT grating absolute diffraction efficiencies of 50% or higher.     

Color holography using the angular selectivity of volume recording media

A display hologram of an object can be recorded and reconstructed in three primary colors if the angular selectivity of volume recording media is exploited. Three holograms are recorded in the same medium, each at a different primary color. These three holograms are reconstructed by simultaneous illumination of the hologram with the original reference beams. By proper choice of the angles that the reference beams make to the hologram, it is possible to suppress strongly cross talk between the different reconstructions (e.g., the red object reconstruction in green light). The technique exhibits high resolution, high diffraction efficiency, and vivid colors. Through the addition of three holographically recorded volume gratings it is possible to reconstruct the hologram with a beam of white light. The saturation and brightness of each primary color in the reconstruction can be adjusted by selection of an appropriate thickness for the corresponding grating.     

Characterization of strong fiber Bragg gratings using an applied thermal chirp and iterative algorithm

Coupling coefficients of various grating types and strengths are calculated from measurements of the complex reflectivity using an applied thermal chirp and optical frequency domain reflectometry (OFDR). The complex reflectivity is then utilized by a layer peeling algorithm to determine the coupling coefficient of the thermally chirped grating. A guess of the temperature profile enables the coupling coefficient of the unchirped grating to be estimated. An iterative algorithm is then used to converge on the exact coupling coefficient, employing an error minimization method applied to the reflectivity spectra. This technique removes the need for a reference grating while preserving the spatial resolution obtained with the initial OFDR measurement. Successful reconstruction of gratings with integrated |κ|L ~ 9.0 are demonstrated with a spatial resolution of less than 100 μm.     

Inverse scattering algorithm for reconstructing lossy fiber Bragg gratings

We demonstrate an inverse scattering algorithm for reconstructing the structure of lossy fiber Bragg gratings. The algorithm enables us to extract the profiles of the refractive index and the loss coefficient along the grating from the grating transmission spectrum and from the reflection spectra, measured from both sides of the grating. Such an algorithm can be used to develop novel distributed evanescent-wave fiber Bragg sensors that measure the change in both the refractive index and the attenuation coefficient of the medium surrounding the grating. The algorithm can also be used to analyze and to design fiber Bragg gratings written in fiber amplifiers. A novel method to overcome instability problems in extracting the parameters of the lossy grating is introduced. The new method also makes it possible to reduce the spectral resolution needed to accurately extract the grating parameters.     

Long-period grating fabricated by periodically tapering standard single-mode fiber

We fabricated an asymmetric long-period grating (LPG) by periodically tapering a section of standard single-mode fiber using a resistive filament heating. The LPG exhibits large peak transmission attenuation of -30.31 dB with only 22 periods in a 1.0 cm long optical fiber and possesses unique characteristics for sensing applications. The bending and strain sensitivities are 1.74 nm m and 1.11 pm/mu epsilon, respectively. The polarization dependent loss is large, up to 11.65 dB, which is caused by an asymmetric index profile in the cross section of the tapered LPG.